It is proposed to construct analytic theories, perform model rate calculations, and to undertake computer simulations of proton and hydride transfer reactions in solution and in models of enzyme systems. Despite their importance in acid-base chemistry and enzyme catalysis, these reactions are not well understood at the molecular level; no theory currently exists which properly addresses such key features as quantum tunneling and the strong coupling of proton and hydride motion to a polar and ionic environment. These aspects can lead to serious departures from the conventional theoretical framework widely employed in the interpretation of kinetic isotope effects. General goals are to provide the theoretical framework for the interpretation of these reactions, to determine the role of tunneling and the environment in their reaction rates, and to predict the experimental trends which probe and reveal their molecular character. Specific aims are to construct the theory of and perform calculations for intramolecular and intermolecular proton and hydride transfers in polar solvents, and to calculate the dependence of the rate constants on isotopic substitution, tem- perature and solvent polarity and dynamics. A related theory will be developed for these transfers in general polar and ionic environments and applied to a model of a critical proton transfer step in a particular enzyme catalysis, and to a hydride transfer in a model of aspects of an enzymatic redox process. These goals will be accomplished via the use and extension of theoretical methodologies successful in the treatment of other types of charge transfer reactions. These include time correlation function methods and Molecular Dynamics computer simulation. Available ab initio potential surface information will also be used.